A line segment goes from #(3 ,1 )# to #(2 ,4 )#. The line segment is dilated about #(2 ,2 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-1#, in that order. How far are the new endpoints form the origin?

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Answer 1 · 2018-04-12T04:32:06

#color(indigo)("Distances of A and B from origin after dilation and reflection "#

#color(indigo)(3.16, 12.65 " respectively"#

#A (3,1), B (2,4), " dilated about C(2,2) by a factor of 3"#

#A' (x,y) =3 * A(x,y) - C (x,y) =(( 9 ,3) - (2,2)) = (7,1)#

#B'(x,y) = 3 ^ B (x,y) - C(x,y) = ((6,12) - (2,2)) = (4,10)#

#color(brown)("reflect thru " x = 4, y = -1, h=4, k= -1. (2h-x, 2k-y)"#

#A''(x,y) = (2h-x, 2k-y) = ((8 - 7), (-2-1)) = (1,-3)#

#"similarly " B''(x,y) = ((8-4),(-2-10)) = (4, -12)#

#bar(A''O) = sqrt(1^2 + 3^2) = sqrt 10 = 3.16#

#bar(B''O) = sqrt(4^2 + 12^2) = sqrt 160 = 12.65#